Question

Prove that√2+√ 5 is irrational

Answer 1

Step-by-step explanation:

Let us suppose that(√2+√5) is rational.

Let (√2+√5) = a, where a is a rational number.

Then, √2 = (a - √5) ........………… (1)

On squaring both sides of (1),we get

2 = a^2 +5 - 2a√5

2a√5 = a^2 +3

√5 = (a^2 +3) /2a ………........(2)

This is impossible, as the right hand side is rational ,while √5 is irrational.

This is a contradiction.

Since the contradiction arises by assuming that (√2+√5) is rational, hence (√2+√5) is irrational.